Question

Em chỉ cần phần c thôi ạ

Answer 1

\(A=\dfrac{1}{200\cdot199}-\dfrac{1}{199\cdot198}-\dfrac{1}{198\cdot197}-...-\dfrac{1}{3\cdot2}-\dfrac{1}{2\cdot1}\)

\(=\dfrac{1}{199}-\dfrac{1}{200}-\left(1-\dfrac{1}{2}-...+\dfrac{1}{198}-\dfrac{1}{199}\right)\)

\(=\dfrac{1}{199}-\dfrac{1}{200}-1+\dfrac{1}{199}\)

\(=\dfrac{-39599}{39800}\)

Answer 2

Bn chụp thiếu rồi!

Answer 3

\(\dfrac{1}{200.199}-\dfrac{1}{199.198}-\dfrac{1}{198.197}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

\(=-\left(\dfrac{1}{200.199}+\dfrac{1}{199.198}+\dfrac{1}{198.197}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)=-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{197.198}+\dfrac{1}{198.199}+\dfrac{1}{199.200}\right)=-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{197}-\dfrac{1}{198}+\dfrac{1}{198}-\dfrac{1}{199}+\dfrac{1}{199}-\dfrac{1}{200}\right)=-\left(1-\dfrac{1}{200}\right)=\dfrac{1}{200}-1=-\dfrac{199}{200}\)

Answer 4

\(A=\dfrac{1}{200.199}-\dfrac{1}{199.198}-\dfrac{1}{198.197}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

\(=\dfrac{1}{200.199}-\left(\dfrac{1}{199.198}+\dfrac{1}{198.197}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)=\dfrac{1}{200.199}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{197.198}+\dfrac{1}{198.199}\right)=\dfrac{1}{199.200}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{197}-\dfrac{1}{198}+\dfrac{1}{198}-\dfrac{1}{199}\right)=\dfrac{1}{199.200}-\left(1-\dfrac{1}{199}\right)=\dfrac{1}{199.200}+\dfrac{1}{199}-1=\dfrac{1+200-199.200}{199.200}=\dfrac{-39599}{39800}\)